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  Assignment No.2 (Course STA301)

Fall 2013 (Total Marks 15)

 

Deadline

Your Assignment must be uploaded/ submitted before or on

February 07 23:59, 2014

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

 

Rules for Marking

It should be clear that your Assignment will not get any credit IF:

  • The Assignment submitted, via email, after due date.
  • The submitted Assignment is not found as MS Word document file.
  • There will be unnecessary, extra or irrelevant material.
  • The Statistical notations/symbols are not well-written i.e., without using MathType software.
  • The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.
  • The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.
  • Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

 

 

Objective(s) of this Assignment:

 

This assignment will strengthen the basic idea about the concept of the following distributions:

  • Poisson distribution
  • Binomial distribution
  • Hypergeometric distribution

 

 

 

 

 

 

 

 

Assignment No: 2 (Lessons 27 – 30)

Question 1:                                                                                             Marks: 4+4=8

a)     A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

b)     In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

 

Question 2:                                                                                             Marks: 4+3=7 

  1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?
  2. The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

 

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a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

  K = 4

  N = 10

  x = 2

  n = 3

       P(X=2) = 0.3           Ans

b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

                   P = 0.36       Ans

                   n = 100        Ans

 

a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

  K = 4

  N = 10

  x = 2

  n = 3

       P(X=2) = 0.3           Ans

b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

                   P = 0.36       Ans

                   n = 100        Ans

 

a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

Question 1

a)      A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

Solution:

When n is greater then 5% of N the hyper geometric formula should be used.

Given:

K = 4

n = 3

N = 10

X = 2

 putting these information in formula of hyper geometric 

ans. is 0.3              

Question 1: 

a)      In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

 Solution:

There is two parameters in binomial p.d. that is n and p and it’s generally denoted by b(x; n,p)

In binomial distribution Mean = E(x) = np

                     And     S.D. =square root npq

Given:

Mean = np = 36

S.D. =  = 4.8

Equations:

np = 36…………(1

 square roor npq= 4.8………(2

For finding the value of n and p

First put the value of np in equation (2)

(square root q36) = 4.8

(root q)6 = 4.8

root q = 4.8/6

 root q= 0.8

q = 0.64

We know that p+q = 1…………(3

For finding the value of ‘p’  put the value of q in equation (3)

P+ 0.64 = 1

P= 1- 0.64

P = 0.36

Now, for finding the value of ‘n’ put the value of p in equation (1)

np = 36

n(0.36)= 36

n = 36 / 0.36

n = 100

So,

p = 0.36

n = 100

Question 2:                                                                                             Marks: 4+3=7 

  1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

is q mai hum binomial formula use kary gay kyon k poisson ki condition satisfy nai ho ri.

poisson k ly 'n' ka 20 say above hona zarori ha

so binomil lagao aur slove kar lo :) 

question 2 (b) mai poisson process wala formula use ho ga kyon condition mai physical thing ki bat ho ri ha aur trails b independent hai

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